Cordray's term would end in July of next year. (AP Photo/Steve Helber, File)

A top Republican lawmaker has threatened Consumer Financial Protection Bureau Director Richard Cordray with contempt if the agency follows through with a rule meant to curb the use of contracts that limit consumers' ability to engage in class-action lawsuits.

House Financial Services Committee Chairman Jeb Hensarling warned Cordray in a letter sent Wednesday that an attempt to follow through with the arbitration rule before responding to a committee subpoena "may lead to contempt proceedings." The Washington Examiner obtained the letter on Friday.

He added that the committee is preparing a report detailing Cordray's "contumacy" in responding to inquiries about the agency's deliberations over the rule and its conversations with outside consumer groups. Those inquiries include a previously unreported subpoena of relevant documents, sent in April.

Hensarling and committee Republicans have long sought the ouster of Cordray, an Obama appointee, through one means or another. Cordray's term would end in July of next year.

The Texas lawmaker has repeatedly called on President Trump to fire Cordray, a measure that would invite a major legal fight.

Meanwhile, committee members have aired harsh criticisms of Cordray, an effort that could lay the groundwork for demonstrating cause for firing him.

In April, for instance, Rep. Sean Duffy of Wisconsin called on Cordray to step down, warning him that the alternative might be an ugly, drawn-out firing. Duffy added that he personally would prefer such a battle, given that it might hurt Cordray's prospects if he runs for governor of Ohio, as Republicans expect him to.